Various techniques exist to reduce maximum eigenfrequencies. These mostly center around modifying the mass matrix. Classical examples are mass-lumping methods, which operate on the consistent mass matrix (in the sense of [1]}, [2]}) to produce a diagonal mass matrix [3]}, [4]}. While the primary advantage of a diagonal mass matrix is that its inversion is trivial, a secondary effect of mass lumping is a reduction of the maximal eigenvalues [5]}. Various lumping strategies exist, such as row-sum lumping (which may lead to negative diagonal values for higher-order serendipity elements, which are catastrophic for numerical simulation) [4]}, diagonal scaling [7]}, lumping by nodal quadrature [8]}, [9]}, [10]} and manifold-based methods [11]}. The approximations underlying these methods imply that the final formulations are not variationally consistent, in the sense of [8]}. As a consequence, the true analytical solution corresponding to the strong form no-longer satisfies the discrete problem statement, resulting in sub-optimal convergence.
